The Non-Topological Origin of the Bending Immunity in Valley Topological Edge States

Valley topological (VT) edge states (ESs), generated at the interface between two two-dimensional C₃ crystals of opposite valley Chern numbers, are renowned for robust wave transport against 120° bending. This bending immunity has been widely recognized as a hallmark of VTESs and one of the manifestations of topological superiority. Here, we revisit the mechanism of the 120° bending immunity by developing a lattice coupled mode theory for the VTESs, combined with a perturbative corner scattering analysis. Our results show that the bending immunity is underpinned by a distinct modal profile of VTESs—momentum hot spots at high-symmetric K (K') points, which is inherited from the bulk band K(K') valleys and is independent of valley topology. This profile ensures the momentum matching between the incident and transmission ESs, contributing to a peculiar supercoupling (SC) effect characterized by extraordinary coupling efficiency and superexponential decay around the corner. Meanwhile, the momentum mismatch between the incident and reflection ESs and the minimal leakage to the corner suppress the reflection. Thus, the high-transmittance bending is realized. Based on this coherent understanding, we propose various bending immune ESs beyond the VT constraint and 120° angular limitation within rhombic lattice photonic crystals. Additionally, the discovery of the superexponential field profile due to the SC effects provides a new approach to engineering the photonic Purcell factor.